Area by DMD, traverse ABCDEA (-5.693)

The latitudes sum to 0.090 m and the departures to 0.000 m. The latitude misclosure of 0.090 m is small (about 1 in 2,000 of the perimeter of about 177 m), so the given figures are used without adjustment.

DMD method

DMD rule (taking the meridian through the starting station):

• DMD of the first line = departure of the first line.

• DMD of any line = DMD of the previous line + departure of the previous line + departure of the line itself.

• DMD of the last line = departure of the last line with opposite sign (a check).

• Double area = Σ (latitude × DMD), and area = ½ |Σ L × DMD|.

• DMD(AB) = D(AB) = -33.990

• DMD(BC) = -33.990 + (-33.990) + (-13.911) = -81.891

• DMD(CD) = -81.891 + (-13.911) + (18.867) = -76.935

• DMD(DE) = -76.935 + (18.867) + (28.608) = -29.460

• DMD(EA) = -29.460 + (28.608) + (0.426) = -0.426

• Check: DMD(EA) = -0.426 = −D(EA) = -0.426, so the DMDs are correct.

$$\text{Area} = \frac{|4056.821|}{2} = 2028.411\ \text{m}^2$$

Answer: Area = 2028.41 m² (0.2028 ha).

(If the latitudes are first balanced by Bowditch's rule, the area changes only slightly, to about 2030 m².)